Since you say you're not much of a needlewoman, find one to help you out. Here in VA a lot of our little dry cleaner shops also do alterations/tailoring. Find one near you/with a good reputation, take the giraffe in and talk to them. Ask if you open it up on a seam and wash it, can they sew it up back up. I would wait while it's being done, don't leave it and come back for it if you can help it.
You also may want to consider replacing or 'supplementing' the stuffing while you have it open. You can buy stuffing of various kinds at your local craft or fabric stores.
This is a short-term solution, so you'll also want to check out the other suggestion to try and buy another or two of the giraffe to keep in reserve.